Q 124. In the following exercises, fact... [FREE SOLUTION]

91影视

Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 7: Q 124. (page 833)

In the following exercises, factor each expression.
$q^{2} - 29 q r - 96 r^{2}$

Short Answer

Expert verified

The factorization of $q^{2} - 29 q r - 96 r^{2}$ is, $(q - 32 r) (q + 3 r)$ .

Step by step solution

Step 1. Given information

Given expression is $q^{2} - 29 q r - 96 r^{2}$ .

Step 2. Find the last terms of the trinomials

Write the factors as trinomials, $q$ in the first term of each binomial and $r$ in the second term.

localid="1649299564676" $(q_r) (q_r)$

Find the numbers that multiply to $- 96$ and add to $- 29$ .

Factors of -96	Sum of factors
-1, 96	-1 + 96 = 95
-2, 48	-2 + 48 = 46
-3, 32	-3 + 32 = 29
-4, 24	-4 + 24 = 20
-6, 10	-6 + 10 = 4
-8, 19	-8 + 19 = 11
-96, 1	-96 + 1 = -95
-48, 2	-48 + 2 = -46
-32, 3	-32 + 3 = -29*
-24, 4	-24 + 4 = 20
-10, 6	-10 + 6 = -4
-19, 8	-19 + 8 = -11

Step 3. Factorization

Use $- 32$ and $3$ as the last terms of the coefficents.

$q^{2} - 29 q r - 96 r^{2} = (q - 32 r) (q + 3 r)$

Step 4. Check

$(q - 32 r) (q + 3 r) = q^{2} - 32 q r + 3 q r - 96 r^{2} = q^{2} - 29 q r - 96 r^{2}$

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91影视

In the following exercises, factor each expression.
$q^{2} - 29 q r - 96 r^{2}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the last terms of the trinomials

Step 3. Factorization

Step 4. Check

One App. One Place for Learning.

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91影视

In the following exercises, factor each expression. q2-29qr-96r2

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the last terms of the trinomials

Step 3. Factorization

Step 4. Check

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Discrete Mathematics

Probability and Statistics

Pure Maths

Applied Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

In the following exercises, factor each expression.
$q^{2} - 29 q r - 96 r^{2}$